Modified Korteweg-de Vries Hierachies in Multiple-Times Variables and the Solutions of Modified Boussinesq Equations

We study solitary-wave and kink-wave solutions of a modified Boussinesq equation through a multiple-time reductive perturbation method. We use appropriated modified Korteweg-de Vries hierarchies to eliminate secular producing terms in each order of the perturbative scheme. We show that the multiple-time variables needed to obtain a regular perturbative series are completely determined by the associated linear theory in the case of a solitary-wave solution, but requires the knowledge of each order of the perturbative series in the case of a kink-wave solution. These appropriate multiple-time variables allow us to show that the solitary-wave as well as the kink-wave solutions of the modified Botussinesq equation are actually respectively a solitary-wave and a kink-wave satisfying all the equations of suitable modified Korteweg-de Vries hierarchies.Comment: RevTex file, submitted to Proc. Roy. Soc. London

Etude par simulation numérique du retraitement des déchets du T.M.S.R. (Thorium Molten Salt Reactor)

Les réacteurs à sels fondus semblent aujourd'hui présenter une alternative intéressante aux réacteurs de quatrième génération refroidis au sodium. En effet, les réacteurs à sels fondus ont beaucoup évolué depuis le M.S.B.R. (prototype américain de réacteur à sels fondus modéré au graphite et fonctionnant en spectre thermique). Le concept évolue aujourd'hui vers des réacteurs sans modérateur en coeur dont le spectre neutronique s'est considérablement durci par rapport au spectre thermique du M.S.B.R. Ces réacteurs possèdent une unité de retraitement couplée qui permet de purifier le sel et d'optimiser la gestion des déchets rejetés. On espère ainsi définir un retraitement efficace qui minimiserait la radiotoxicité de ce type de réacteur. Ce rapport explique comment on simule l'évolution des réacteurs à sels fondus et on calcule la radiotoxicité des déchets produits. Les résultats donnés ici ne sont qu'indicatifs et servent surtout à monter que les outils et méthodes développés pendant ce stage sont satisfaisants et permettront une étude beaucoup plus poussée lors de la thèse qui suit

Minimizing the fissile inventory of the molten salt fast reactor

International audienceMolten salt reactors in the configurations presented here, called Molten Salt Fast Reactors (MSFR), have been selected for further studies by the Generation IV International Forum. These reactors may be operated in simplified and safe conditions in the Th/233U fuel cycle with fluoride salts. We present here the concept, before focusing on a possible optimization in term of minimization of the initial fissile inventory. Our studies demonstrate that an inventory of 233U lower than 4 metric tons per GWe may be easily reached, and bring to light the limitations of the concept due to the irradiation damages to the structural materials and to the capacities of the heat exchangers. We conclude that these two issues will have to be studied in depth to allow a realistic evaluation of the global possibilities of such a reactor

An investigation of the changes in binocular accommodative rock performance as a function of spherical lenses

This study has been conducted to determine the change in cycles per minute as a function of dioptric change in lens power on the plus and minus binocular accommodative rock

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

By considering the long-wave limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple scale method in obtaining uniform perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E

Reactor Neutrino Experiments with a Large Liquid Scintillator Detector

We discuss several new ideas for reactor neutrino oscillation experiments with a Large Liquid Scintillator Detector. We consider two different scenarios for a measurement of the small mixing angle $\theta_{13}$ with a mobile $\bar{\nu}_e$ source: a nuclear-powered ship, such as a submarine or an icebreaker, and a land-based scenario with a mobile reactor. The former setup can achieve a sensitivity to $\sin^2 2\theta_{13} \lesssim 0.003$ at the 90% confidence level, while the latter performs only slightly better than Double Chooz. Furthermore, we study the precision that can be achieved for the solar parameters, $\sin^2 2\theta_{12}$ and $\Delta m_{21}^2$, with a mobile reactor and with a conventional power station. With the mobile reactor, a precision slightly better than from current global fit data is possible, while with a power reactor, the accuracy can be reduced to less than 1%. Such a precision is crucial for testing theoretical models, e.g. quark-lepton complementarity.Comment: 18 pages, 3 figures, 2 tables, revised version, to appear in JHEP, Fig. 1 extended, Formula added, minor changes, results unchange

Asymptotic dynamics of short-waves in nonlinear dispersive models

The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation can propagates short-waves. This result contradict the Benjamin hypothesis that short-waves tends not to propagate in this model and close a part of the old controversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine equations. We shown that a nonlinear (quadratic) Klein-Gordon type equation substitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation of long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon equations are understood as an all orders asymptotic behaviour of short-waves. It is proved that the antikink solution of phi-4 model which was never obtained perturbatively can be obtained by perturbation expansion in the wave-number k in the short-wave limit.Comment: to appears in Physical Review E. 4 pages, revtex file